Transcript Matt`s talk about our observation of quantum

Observation of High-order Quantum
Resonances in the Kicked Rotor
Jalani F. Kanem1, Samansa Maneshi1,
Matthew Partlow1, Michael Spanner2
and Aephraim Steinberg1
Center for Quantum Information
& Quantum Control,
Institute for Optical Sciences,
1Department of Physics,
2Department of Chemistry,
University of Toronto
INTRODUCTION
• The quantum kicked rotor is a rich system for studying
quantum-classical correspondence, decoherence, and
quantum dynamics in general
• Atom optics systems provide excellent analogue:
Atom Optics Realization of the Quantum Delta-Kicked Rotor
Raizen group - PRL 75, 4598-4601 (1995)
• Possible probe of lattice inter-well coherence ?
Outline:
•
•
•
•
Kicked Rotor analogue with optical lattice
Quantum resonances
Experimental setup
Data & simulations
Ideal Delta Kicked Rotor
Optical Lattice realization
Kicked Rotor
ideal
g
lattice implementation

T
Ideal Rotor
Atom optics realization
Kicked Rotor
ideal
g
lattice implementation

T
Scaled quantum Schrödinger’s:
Stochasticity parameter: system becomes chaotic when strength
or period of kicks are large enough that atoms (rotor) travel more
than one lattice spacing (2 between kicks.→Force on atom is a
random variable
Scaled Planck's constant is a measure of how 'quantum' the system is.
The smaller , the greater the quantum classical correspondence
~ ratio of quantized momentum transfer from lattice
to momentum
required to move one lattice spacing in one kick period, T
Discuss classical vs. quantum behaviour of momentum
diffusion?
Classically chaotic: momentum diff. ~ N1/2
Quantum: dynamic localization and/or quantum resonance
Quantum Resonances
•
•
Resonances → dramatically increased energy absorption
Due to rephasing of momentum states coupled by the lattice potential whose
momentum differ by a multiple of
:
•
2π, 4π, etc. ‘easy’ to observe: all momentum states rephase e.g. wavepacket
revival
High-order resonance, s>1, fractional revival, only some quasimomentum
states rephase.
•
Experimental Setup
AOM2
PBS
TUI
Amplifier
Grating Stabilized
Laser
AOM1

PBS
Note: optical standing wave is
in vertical direction
‘hot’ un-bound atoms fall out
before kicking begins
Spatial filter
Function
Generator
1m
~3 recoil energies
Tilted due to gravity
PBS
Individual control of frequency
and phase of AOMs allows
control of lattice velocity and
position.
A tilted lattice would affect the
dynamics of the experiment, therefore
we accelerate the lattice downward at
g to cancel this effect.
The System
Preparation:
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85Rb
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108 atoms
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Cooled to ~10K
vapor cell MOT
Load a 1-D optical lattice
supporting 1-2 bound
states (~14 recoil energies)
Typical pulse parameters:
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50-150s pulse period
●
5-15s pulse length
Depth of 30-180 recoil units
(~2-12K)
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Initial rms velocity width
of ~5mm/s (255nK)
●
●
chaos parameter  = 1-10
●
scaled Planck's constant
=1-10
Past experiments with thermal clouds
Raizen reference
And
Reference paper that
figure is from
2π
4π
Our observed resonances
Inset: calculation of resonance-independent quantum diffusion
(How much to explain? Make extra slide?)
Quantum, not classical: resonance position insensitive to kick strength
/π = 0.47±0.01, 0.72±0.01, 1, 1.25±0.02, 1.54±0.02
Simulations
Describe widths used for
simulations
interesting conclusion ?
Conclusions
• have observed high-order quantum resonances in
atom-optics implementation of the kicked rotor
• visibility due to using lattice to select out cold atoms
• possibly greater coherence across lattice than
we expect?
•give credit to other observation
•in the future, control and measurement of
quasimomentum
This work: arXiv:quant-ph/0604110
EXTRAS
a
Windell Oskay/University of Texas at Austin
Energy growth / resonance resolution
Quadratic growth ???